Introducing the noiseless part of observation given in (REF ) as \(\mu  = \rho e^{\jmath \phi }\sqrt{P_t}\mathbf {d}(\,\tau )\,\mathbf {b}^\top \mathbf {\Gamma }\)  , and
the \(6\times 1\)  vector of unknowns \(\eta  = [\rho \quad \phi \quad \tau \quad \mathbf {p}_{\text{ris}}^\top \quad \alpha ]^\top \) , and \(\zeta  = \left[\rho \quad \phi \quad \mathbf {p}_{\text{ris}}^\top \quad \alpha \right]^\top \) , the FIM \(\mathbf {J}(\eta ) \in \mathbb {R}^{6\times 6}\)  is defined as [1]}
\(\mathbf {J}(\eta )= \frac{2}{\sigma ^2} \sum _{t=1}^T\sum _{n_c=1}^{N_c} \Re \Bigg \lbrace \frac{ \partial [\mu ]_{t,n_c}}{\partial \eta } \left( \frac{ \partial [\mu ]_{t,n_c}}{\partial \eta }\, \right)^{\mathsf {H}}\, \Bigg \rbrace .\) 
